A recent break-through was obtained by Buckmaster-Vicol [1]}
for the 3D incompressible NSE,
to which the non-uniqueness of weak solutions was proved
by an \(L_x^2\) -based intermittent convex integration scheme.
Luo-Titi [2]} then proved the non-uniqueness results for the 3D hyperviscous NSE (REF ),
whenever \({\alpha }\)  is less than the Lions exponent, i.e., \(\alpha \in (1,5/4)\) .
Moreover, Luo-Qu [3]} proved the non-uniqueness for the 2D hypoviscous NSE with \({\alpha }\in (0,1)\) .
The non-uniqueness results
for the stationary NSE were proved by Cheskidov-Luo [4]}, [5]}.
We also refer to the works by Jia-Šverák [6]}, [7]} for
another method for the non-uniqueness issue of Leray-Hopf
solutions in \(L^{\infty }_tL^3_x\)  under a certain assumption for the linearized Navier-Stokes operator,
and Colombo-De Lellis-De Rosa[8]} and De Rosa[9]}
for the non-uniqueness of Leray weak solutions to hypoviscous NSE with small viscosity.
